Preheat the oven to 375 degrees F.
Prepare the piecrust and line a deep, 10-inch, removable bottom tart pan with 1 of the crusts.
In a large bowl, combine the apples, walnuts, 1/2 cup sugar, brown sugar, lemon juice, flour, cinnamon, nutmeg, and salt. Toss to coat the apples with the other ingredients and let sit for 10 minutes.
Spoon the apple mixture into the prepared pie pan and dot the fruit with the butter slivers. Top with the 2nd crust. Using a sharp knife, cut away the excess dough. Crimp the edges of the pie firmly to seal the dough. With a sharp knife, cut a decorative pattern of slits into the top crust. With a pastry brush, brush the cream over the top crust, and sprinkle the remaining 2 teaspoons of sugar over the top.
Bake until the crust is golden and the juices begin to bubble, about 45 minutes to 1 hour. Remove from the oven and let cool at least 1 hour before serving.
Preheat a griddle.
To serve, slice the pie into 8 equal portions. Melt the remaining 2 tablespoons of butter on the griddle. Add the pie, and top each slice with a slice of cheese. Cook until the cheese melts and the bottom crust is golden brown, about 2 to 3 minutes. Serve hot with a scoop of vanilla ice cream on top.
Yield: 8 servings